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Requirements for fission

  1. Nov 11, 2012 #1
    So I think, as a rule of thumb that for fission to be possible [itex]\frac{Z^2}{A}[/itex][itex]\geq[/itex]47

    I want to be able to derive this relationship though..

    If a nucleus deforms into an ellipsoid, its surface area can be described by

    4[itex]\pi[/itex]R2(1+[itex]\frac{2}{5}[/itex][itex]\epsilon^2[/itex] + ...) call this X

    And its Coulomb energy can be described as

    [itex]\frac{3Z^2}{20\pi\epsilon_0R}[/itex](1-[itex]\frac{1}{5}[/itex][itex]\epsilon^2[/itex] + ...) call this Y

    And so ΔBE = X-Y

    For fission to occur set ΔBE ≤ 0

    Once I've done all this I'm not sure how to get ΔBE in terms of A and Z only. I know R = r0A1/3

    thanks
     
  2. jcsd
  3. Nov 11, 2012 #2
    I should mention that [itex]\epsilon[/itex] is an arbitrary deformation parameter associated with the ellipsoid and can be factored out
     
  4. Nov 12, 2012 #3

    mfb

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    Staff: Mentor

    You can use that formula for R and solve for ##\frac{\partial (X-Y)}{\partial \epsilon}=0##.
    I would expect that this overestimates the required Z^2/A - if that derivative is negative, the nucleus should not form at all or decay within less than a femtosecond.
     
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